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Plasticity Theory
Flow plasticity is a solid mechanics theory that is used to describe the plastic behavior of materials. Flow plasticity theories are characterized by the assumption that a flow rule exists that can be used to determine the amount of plastic deformation in the material. In flow plasticity theories it is assumed that the total strain in a body can be decomposed additively (or multiplicatively) into an elastic part and a plastic part. The elastic part of the strain can be computed from a linear elastic or hyperelastic constitutive model. However, determination of the plastic part of the strain requires a flow rule and a hardening model. Small deformation theory Typical flow plasticity theories for unidirectional loading (for small deformation perfect plasticity or hardening plasticity) are developed on the basis of the following requirements: # The material has a linear elastic range. # The material has an elastic limit defined as the stress at which plastic deformation f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prager Consistency Condition
Prager (variants: Praeger, Preger) is a surname, which may refer to: Prager * David Prager (born 1977), American TV producer and blogger * Dennis Prager (born 1948), U.S. conservative radio talk show host, columnist and public speaker ** PragerU, a right-wing conservative non-profit organization that creates videos on various political, economic and philosophical topics * Felice Prager (born 1953), nee Klein, U.S. author, journalist, educational therapist * Joshua P. Prager (born 1949), US physician * Joshua Harris Prager, US journalist * Mark Prager Lindo (1819–1879), Anglo-Dutch prose writer of English-Jewish descent * Richard Prager (1883–1945), German-American astronomer * Richard Prager (skier), West German para-alpine skier * Susan Westerberg Prager (born 1942), Association of American Law Schools Executive Vice President and Executive Director from 2008 * Walter Prager (1910–1984), Swiss alpine skier * William Prager (1903–1980), German-born US physicist Fictional ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stress Measures
In continuum mechanics, the most commonly used measure of stress is the Cauchy stress tensor, often called simply ''the'' stress tensor or "true stress". However, several alternative measures of stress can be defined: #The Kirchhoff stress (\boldsymbol). #The Nominal stress (\boldsymbol). #The first Piola–Kirchhoff stress (\boldsymbol). This stress tensor is the transpose of the nominal stress (\boldsymbol = \boldsymbol^T). #The second Piola–Kirchhoff stress or PK2 stress (\boldsymbol). #The Biot stress (\boldsymbol) Definitions Consider the situation shown in the following figure. The following definitions use the notations shown in the figure. In the reference configuration \Omega_0, the outward normal to a surface element d\Gamma_0 is \mathbf \equiv \mathbf_0 and the traction acting on that surface (assuming it deforms like a generic vector belonging to the deformation) is \mathbf_0 leading to a force vector d\mathbf_0. In the deformed configuration \Omega, the surfac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mandel Stress
Mandel is a surname (and occasional given name) that occurs in multiple cultures and languages. It is a Dutch, German and Jewish surname, meaning "almond", from the Middle High German and Middle Dutch ''mandel''.''Dictionary of American Family Names''"Mandel Family History" Oxford University Press, 2013. Retrieved on 18 January 2016. Mandel can be a locational surname, from places called Mandel, such as Mandel, Germany. Mandel may also be a Dutch surname, from the Middle Dutch ''mandele'', meaning a number of sheaves of harvested wheat. Notable people *Alon Mandel (born 1988), Israeli swimmer *Babaloo Mandel (born 1949), American screenwriter *David Mandel (born 1970), American television producer and writer *Edgar Mandel (born 1928), German actor *Eli Mandel (1922–1992), Canadian writer *Emily St. John Mandel (born 1979), Canadian novelist * Emmanuil Mandel (1925–2018), Russian poet *Ernest Mandel (1923–1995), Belgian politician, professor and writer *Frank Mandel, America ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logarithmic Strain
In physics, deformation is the continuum mechanics transformation of a body from a ''reference'' configuration to a ''current'' configuration. A configuration is a set containing the positions of all particles of the body. A deformation can occur because of external loads, intrinsic activity (e.g. muscle contraction), body forces (such as gravity or electromagnetic forces), or changes in temperature, moisture content, or chemical reactions, etc. Strain is related to deformation in terms of ''relative'' displacement of particles in the body that excludes rigid-body motions. Different equivalent choices may be made for the expression of a strain field depending on whether it is defined with respect to the initial or the final configuration of the body and on whether the metric tensor or its dual is considered. In a continuous body, a deformation field results from a stress field due to applied forces or because of some changes in the temperature field of the body. The relati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cauchy-Green Deformation Tensor
In continuum mechanics, the finite strain theory—also called large strain theory, or large deformation theory—deals with deformations in which strains and/or rotations are large enough to invalidate assumptions inherent in infinitesimal strain theory. In this case, the undeformed and deformed configurations of the continuum are significantly different, requiring a clear distinction between them. This is commonly the case with elastomers, plastically-deforming materials and other fluids and biological soft tissue. Displacement The displacement of a body has two components: a rigid-body displacement and a deformation. * A rigid-body displacement consists of a simultaneous translation (physics) and rotation of the body without changing its shape or size. * Deformation implies the change in shape and/or size of the body from an initial or undeformed configuration \kappa_0(\mathcal B) to a current or deformed configuration \kappa_t(\mathcal B) (Figure 1). A change in the confi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compatibility (mechanics)
In continuum mechanics, a compatible deformation (or strain) tensor field in a body is that ''unique'' tensor field that is obtained when the body is subjected to a continuous, single-valued, displacement field. Compatibility is the study of the conditions under which such a displacement field can be guaranteed. Compatibility conditions are particular cases of integrability conditions and were first derived for linear elasticity by Barré de Saint-Venant in 1864 and proved rigorously by Beltrami in 1886.C Amrouche, PG Ciarlet, L Gratie, S Kesavan, On Saint Venant's compatibility conditions and Poincaré's lemma, C. R. Acad. Sci. Paris, Ser. I, 342 (2006), 887-891. In the continuum description of a solid body we imagine the body to be composed of a set of infinitesimal volumes or material points. Each volume is assumed to be connected to its neighbors without any gaps or overlaps. Certain mathematical conditions have to be satisfied to ensure that gaps/overlaps do not de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Strain Theory
In continuum mechanics, the finite strain theory—also called large strain theory, or large deformation theory—deals with deformations in which strains and/or rotations are large enough to invalidate assumptions inherent in infinitesimal strain theory. In this case, the undeformed and deformed configurations of the continuum are significantly different, requiring a clear distinction between them. This is commonly the case with elastomers, plastically-deforming materials and other fluids and biological soft tissue. Displacement The displacement of a body has two components: a rigid-body displacement and a deformation. * A rigid-body displacement consists of a simultaneous translation (physics) and rotation of the body without changing its shape or size. * Deformation implies the change in shape and/or size of the body from an initial or undeformed configuration \kappa_0(\mathcal B) to a current or deformed configuration \kappa_t(\mathcal B) (Figure 1). A change in the conf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crystal Plasticity
Crystal plasticity is a mesoscale computational technique that takes into account crystallographic anisotropy in modelling the mechanical behaviour of Crystallite, polycrystalline materials. The technique has typically been used to study deformation through the process of Slip (materials science), slip, however, there are some flavors of crystal plasticity that can incorporate other deformation mechanisms like Crystal twinning , twinning and phase transformations. Crystal plasticity is used to obtain the relationship between stress and strain that also captures the underlying physics at the crystal level. Hence, it can be used to predict not just the Stress–strain curve, stress-strain response of a material, but also the Texture (crystalline), texture evolution, Micromechanics , micromechanical field distributions, and regions of strain localisation. The two widely used formulations of crystal plasticity are the one based on the finite element method known as Crystal Plastici ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proceedings Of The Royal Society A
''Proceedings of the Royal Society'' is the main research journal of the Royal Society. The journal began in 1831 and was split into two series in 1905: * Series A: for papers in physical sciences and mathematics. * Series B: for papers in life sciences. Many landmark scientific discoveries are published in the Proceedings, making it one of the most historically significant science journals. The journal contains several articles written by the most celebrated names in science, such as Paul Dirac, Werner Heisenberg, Ernest Rutherford, Erwin Schrödinger, William Lawrence Bragg, Lord Kelvin, J.J. Thomson, James Clerk Maxwell, Dorothy Hodgkin and Stephen Hawking. In 2004, the Royal Society began ''The Journal of the Royal Society Interface'' for papers at the interface of physical sciences and life sciences. History The journal began in 1831 as a compilation of abstracts of papers in the ''Philosophical Transactions of the Royal Society'', the older Royal Society publication, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
